Final answer:
To simplify (24x³-8x²)/(4x²), cancel out common factors to get 6x-2. This process is similar to subtracting exponents when dividing powers of ten.
Step-by-step explanation:
To divide the expression (24x³-8x²)/(4x²), we can simplify by cancelling terms and reducing the fraction. Since both terms in the numerator have a factor of 8x², and the denominator is 4x², we can simplify as follows:
(24x³-8x²) / (4x²)
= (8x²(3x-1)) / (4x²)
= 2(3x-1)
= 6x-2
We divided the coefficients (24 and 8 by 4) and cancelled out the x² terms. This process is analogous to how we subtract exponents when dividing powers of ten. Recall that dividing numbers with powers of ten involves subtracting the exponent in the denominator from that in the numerator. In our case, since the x² is in both the numerator and denominator, they cancel out, which is like subtracting their exponents.